Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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### Triangle Classification Problem A triangle with side lengths \(2\), \(4\sqrt{6}\), and \(10\) is what type of triangle? **Options**: a) Acute b) Right c) There is not enough information to determine the answer. d) Obtuse To solve this, we need to apply the triangle inequality theorem and Pythagorean theorem. **Triangle Inequality Theorem**: The sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. Check: - \(2 + 4\sqrt{6} > 10\) - \(2 + 10 > 4\sqrt{6}\) - \(4\sqrt{6} + 10 > 2\) **Pythagorean Theorem for Right Triangles**: To determine if the triangle is right, check if \(a^2 + b^2 = c^2\), where \(c\) is the longest side. **Comparisons for Acuteness or Obtuseness**: - If \(a^2 + b^2 > c^2\), the triangle is acute. - If \(a^2 + b^2 < c^2\), the triangle is obtuse. You can verify these conditions to determine the correct type of triangle.
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Transcribed Image Text:### Triangle Classification Problem A triangle with side lengths \(2\), \(4\sqrt{6}\), and \(10\) is what type of triangle? **Options**: a) Acute b) Right c) There is not enough information to determine the answer. d) Obtuse To solve this, we need to apply the triangle inequality theorem and Pythagorean theorem. **Triangle Inequality Theorem**: The sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. Check: - \(2 + 4\sqrt{6} > 10\) - \(2 + 10 > 4\sqrt{6}\) - \(4\sqrt{6} + 10 > 2\) **Pythagorean Theorem for Right Triangles**: To determine if the triangle is right, check if \(a^2 + b^2 = c^2\), where \(c\) is the longest side. **Comparisons for Acuteness or Obtuseness**: - If \(a^2 + b^2 > c^2\), the triangle is acute. - If \(a^2 + b^2 < c^2\), the triangle is obtuse. You can verify these conditions to determine the correct type of triangle.
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